We are continuing our studies of the folding properties of single-domain proteins using [unreadable] simple statistical-mechanical models. In these models it is assumed that the folding [unreadable] properties of a protein are determined entirely by the intramolecular interactions present [unreadable] in its native folded conformation. Proteins are represented as chains of monomer units [unreadable] (corresponding to amino acid residues) each of which has only two possible [unreadable] conformational states, the "native" state, corresponding to the conformation assumed by [unreadable] the unit in the native structure of the chain, and the "random-coil" state, which [unreadable] encompasses all non-native conformations. The structural states of a polypeptide chain [unreadable] are then defined by the sequence of native/random-coil states of these monomers. The [unreadable] stability of any such state of the chain is determined by the offsetting effects of the [unreadable] destabilizing entropy losses associated with fixing monomers in the native conformation, [unreadable] and the stabilizing native non-bonding contacts between different parts of the chain. The [unreadable] map of native contacts is derived from the X-ray crystallographic or NMR-derived [unreadable] structure of the corresponding protein. In the simplest picture, a state with a specified [unreadable] sequence of native/random-coil monomers may only form those native contacts that [unreadable] connect parts of the chain lying in the same contiguous stretch of native monomers. In a [unreadable] more complete picture, contacts are also possible between parts of the chain separated by [unreadable] intervening stretches of non-native monomers and induce an additional destabilizing [unreadable] entropy loss by constraining the ends of the loops of random-coil chain formed by these [unreadable] non-native stretches. For a model protein of a given length and a specified set of [unreadable] structurally-derived native contacts, it is possible in principle to explicitly construct all [unreadable] possible sequences of monomer native/random-coil states. For specified values for the [unreadable] entropy losses of fixing a single unit in the native conformation and of closing loops of [unreadable] non-native chain, and for the energy of the intra-chain contacts, it is possible to compute [unreadable] the stabilities of all such sequences and thereby compute a model partition function of the [unreadable] chain. The intractably large number of states that arises from complete enumeration of [unreadable] the possible combinations of monomer states for typical chain lengths has motivated the [unreadable] calculation of partition functions in the so-called "single-sequence", "double-sequence", [unreadable] and "triple-sequence" approximations, in which only states which have at most one, two, [unreadable] or three contiguous stretches of native monomers, respectively, are included. These [unreadable] partition functions are used to compute the free energy for a given chain as a function of [unreadable] a single reaction coordinate defined for each state as either the total number of native [unreadable] monomers or the fraction of native contacts formed in that state; this "reaction free-[unreadable] energy surface" provides the basis for modeling the equilibrium and kinetic folding [unreadable] properties of the chain. In work reported in previous years, we used a "combinatorial [unreadable] modeling" procedure within this framework to identify which among a wide variety of [unreadable] possible model assumptions and features consistently produce the most accurate [unreadable] descriptions of the measured folding properties of a set of two-state proteins. More [unreadable] recently, we have been using the best-performing of these models to directly analyze an [unreadable] extensive set of equilibrium and kinetic measurements performed in our own laboratory [unreadable] of the folding of the single alpha-helical protein villin. Among the measurements being [unreadable] modeled is the equilibrium temperature dependence of the UV circular dichroism, which [unreadable] reflects the extent of alpha-helix formation concomitant with the folding process; in our [unreadable] model the helical content of each state of the protein chain is simply the combined [unreadable] lengths of contiguous stretches of native monomers in parts of the sequence that are [unreadable] helical in the native state. We also analyze both the equilibrium temperature dependence [unreadable] and the T-jump kinetics of the UV fluorescence, which probes the formation of locally [unreadable] compact protein structures through the degree of quenching of the fluorescence of the [unreadable] single tryptophan sidechain by contact with residues elsewhere in the chain; model states [unreadable] in which the fluorescence is quenched are precisely those in which a native contact [unreadable] between the tryptophan and the quenching residue(s) is formed. Most recently we have [unreadable] incorporated into our analysis the model-based calculation of heat-capacity changes of [unreadable] villin as temperature is varied through the thermal folding/unfolding transition, in order [unreadable] to analyze differential scanning calorimetry measurements (in collaboration with the [unreadable] group of Jose M. Sanchez-Ruiz of the University of Granada in Spain). Preliminary [unreadable] results indicate that our simple model picture for the enumeration and stabilities of the [unreadable] various states of the protein chain, combined with a straightforward prescription for [unreadable] computing the spectroscopic properties of the individual states, describes quite well the [unreadable] equilibrium and kinetic spectroscopic measurements of the folding properties of this [unreadable] protein. [unreadable] In keeping with our interest in developing and exploiting new methods for probing the [unreadable] structural dynamics of macromolecules, we are collaborating with Philip Anfinrud's [unreadable] group in the Laboratory of Chemical Physics in the development of new algorithms for [unreadable] the analysis of Laue (i.e., polychromatic illumination) diffraction data acquired in time-[unreadable] resolved X-ray crystallographic studies of proteins. These algorithms include efficient [unreadable] procedures for the assignment of Miller indices to observed reflections, the integration of [unreadable] intensities to produce structure factors for these reflections, and the scaling of the [unreadable] resulting sets of structure factors from multiple images onto a common intensity scale. [unreadable] We have also created a fundamentally new prescription for extracting more accurate [unreadable] structure-factor information from the distributions of pixel intensities within the [unreadable] individual spots in a Laue diffraction image, based on a model description of the [unreadable] distribution of mosaic structures actually present in the crystal.